Skip to main content
Log in

Landau–Zener–Stückelberg–Majorana interference of a spin-orbit-coupled Bose–Einstein condensate

  • Regular Article - Cold Matter and Quantum Gases
  • Published:
The European Physical Journal D Aims and scope Submit manuscript

Abstract

The spin-orbit-coupled (SOC) ultracold atomic gases provide unique opportunities for exploring exotic quantum phases and introduce new capabilities into the quantum simulation. In this paper, we study the coherent control of spin states in SOC Bose–Einstein condensate (BEC) by exploiting and implementing the general concept of Landau–Zener–Stüeckelberg–Majorana (LZSM) interference. For a SOC BEC, the Landau–Zener (LZ) transition between the dressed eigenlevels occurs as the BEC is accelerated through the SOC-avoided crossing, which corresponds to a breakdown of the spin momentum locking. In our scheme, two LZ pulses are separated by an intermediate holding period of variable duration. The nice LZSM interference patterns can be generated and controlled by controlling several parameters, corresponding to coherent control of the spin state of the SOC BEC. In particular, the destructive and constructive patterns of LZSM interference are observed and well explained through analytical analysis. Our results suggest a potential application of the LZSM interferometry in calibrating the spin states of a SOC BEC.

Graphic Abstract

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

Data Availability Statement

The manuscript has associated data in a data repository. [Authors’ comment: All relevant data generated in this work have been contained in this published article.]

References

  1. L.D. Landau, Zur theorie der energieubertragung i. Phys. Z. Sowjetunion 1, 46–51 (1932)

    MATH  Google Scholar 

  2. Clarence Zener, Non-adiabatic crossing of energy levels. Proc. R. Soc. London Ser. A 137(833), 696–702 (1932)

    Article  ADS  Google Scholar 

  3. L.D. Landau, Zur theorie der energieubertragung ii. Phys. Z. Sowjetunion 2, 88–95 (1932)

    MATH  Google Scholar 

  4. E.C.G. Stückelberg, Theory of inelastic collisions between atoms. Helv. Phys. Acta 5, 369–422 (1932)

    Google Scholar 

  5. Ettore Majorana, Atomi orientati in campo magnetico variabile. Nuovo Cimento 9, 43–50 (1932)

    Article  Google Scholar 

  6. Francesco Di Giacomo, Evgenii E. Nikitin, The majorana formula and the landauczenercstckelberg treatment of the avoided crossing problem. Sov. Phys. Uspekhi 48, 515 (2005)

    Article  ADS  Google Scholar 

  7. S.N. Shevchenko, S. Ashhab, Franco Nori, Landauczenercstckelberg interferometry. Phys. Rep. 492(1), 1–30 (2010)

    Article  ADS  Google Scholar 

  8. S. Yoakum, L. Sirko, P.M. Koch, Stueckelberg oscillations in the multiphoton excitation of helium rydberg atoms: Observation with a pulse of coherent field and suppression by additive noise. Phys. Rev. Lett. 69, 1919–1922 (1992)

    Article  ADS  Google Scholar 

  9. C.S.E. van Ditzhuijzen, A. Tauschinsky, H.V.L. van den Heuvell, Observation of stückelberg oscillations in dipole-dipole interactions. Phys. Rev. A 80, 063407 (2009)

    Article  ADS  Google Scholar 

  10. L.Y. Gorelik, N.I. Lundin, V.S. Shumeiko, R.I. Shekhter, M. Jonson, Superconducting single-mode contact as a microwave-activated quantum interferometer. Phys. Rev. Lett. 81, 2538–2541 (1998)

    Article  ADS  Google Scholar 

  11. C.M. Quintana, K.D. Petersson, L.W. McFaul, S.J. Srinivasan, A.A. Houck, J.R. Petta, Cavity-mediated entanglement generation via landau-zener interferometry. Phys. Rev. Lett. 110, 173603173603 (2013)

    Article  ADS  Google Scholar 

  12. G.D. Fuchs, V.V. Dobrovitski, D.M. Toyli, F.J. Heremans, D.D. Awschalom, Gigahertz dynamics of a strongly driven single quantum spin. Science 326(5959), 1520–1522 (2009)

    Article  ADS  Google Scholar 

  13. G.D. Fuchs, G. Burkard, P.V. Klimov, D.D. Awschalom, A quantum memory intrinsic to single nitrogencvacancy centres in diamond. Nat. Phys. 7, 789–793 (2011)

    Article  Google Scholar 

  14. Jingfu Zhang, Jeong Hyun Shim, T. Ingo Niemeyer, T. Taniguchi, H. Teraji, S. Abe, T. Onoda, T. Yamamoto, J.Isoya Ohshima, D. Suter, Experimental implementation of assisted quantum adiabatic passage in a single spin. Phys. Rev. Lett. (2013)

  15. M.B. Kenmoe, L.C. Fai, Periodically driven three-level systems. Phys. Rev. B 94 (2016)

  16. Q. Zhang, P. Hänggi, J. Gong, Two-mode bose-einstein condensate in a high-frequency driving field that directly couples the two modes. Phys. Rev. A 77, 053607 (2008)

    Article  ADS  Google Scholar 

  17. Q. Zhang, P. Hänggi, J. Gong, Nonlinear landau-zener processes in a periodic driving field. New J. Phys. 10(7), 073008 (2008)

    Article  ADS  Google Scholar 

  18. Du Lingjie, Minjie Wang, Yu. Yang, Landau-zener-stückelberg interferometry in the presence of quantum noise. Phys. Rev. B 82, 045128 (2010)

    Article  ADS  Google Scholar 

  19. Du Lingjie, Yu. Yang, Noise effects on landau-zener-stückelberg interferometry in multilevel artificial atoms. Phys. Rev. B 82, 144524 (2010)

    Article  Google Scholar 

  20. Boyan T. Torosov, Nikolay V. Vitanov, Pseudo-hermitian landau-zener-stückelberg-majorana model. Phys. Rev. A 96, 013845 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  21. X. Shen, F. Wang, Z. Li, Z. Wu, Landau-zener-stückelberg interferometry in \({\cal{PT}}\)-symmetric non-hermitian models. Phys. Rev. A 100 (2019)

  22. S.C. Li, L.B. Fu, J. Liu, Nonlinear landau-zener-stückelberg-majorana interferometry. Phys. Rev. A 98, 013601 (2018)

  23. Y.-J. Lin, I.B. Jiménez-García, Spielman. Spin-orbit-coupled bose-einstein condensates. Nature 471(7336), 83–86 (2011)

    Article  ADS  Google Scholar 

  24. J.Y. Zhang, S.C. Ji, Z. Chen, L. Zhang, Z.D. Du, B. Yan, G.S. Pan, B. Zhao, Y.J. Deng, H. Zhai, S. Chen, J.W. Pan, Collective dipole oscillations of a spin-orbit coupled bose-einstein condensate. Phys. Rev. Lett. 109, 115301 (2012)

    Article  ADS  Google Scholar 

  25. Qu Chunlei, Chris Hamner, Ming Gong, Chuanwei Zhang, Peter Engels, Observation of zitterbewegung in a spin-orbit-coupled bose-einstein condensate. Phys. Rev. A 88, 021604 (2013)

    Article  ADS  Google Scholar 

  26. A.J. Olson, S.J. Wang, R.J. Niffenegger, C.H. Li, C.H. Greene, Y.P. Chen, Tunable landau-zener transitions in a spin-orbit-coupled bose-einstein condensate. Phys. Rev. A 90, 013616 (2014)

    Article  ADS  Google Scholar 

  27. C. Hamner, Q. Chunlei, Y. Zhang, J. Chang, M. Gong, C. Zhang, P. Engels, Dicke-type phase transition in a spin-orbit-coupled bose-einstein condensate. Nat. Comm. 5, 4023 (2014)

    Article  ADS  Google Scholar 

  28. Z. Wu, L. Zhang, W. Sun, X.T. Xu, B.Z. Wang, S.C. Ji, Y. Deng, S. Chen, X.J. Liu, J.W. Pan, Realization of two-dimensional spin-orbit coupling for bose-einstein condensates. Science 354(6308), 83–88 (2016)

    Article  ADS  Google Scholar 

  29. P. Wang, Z.Q. Yu, Z. Fu, J. Miao, L. Huang, S. Chai, H. Zhai, J. Zhang, Spin-orbit coupled degenerate fermi gases. Phys. Rev. Lett. 109, 095301 (2012)

    Article  ADS  Google Scholar 

  30. L.W. Cheuk, A.T. Sommer, Z. Hadzibabic, T. Yefsah, W.S. Bakr, M.W. Zwierlein, Spin-injection spectroscopy of a spin-orbit coupled fermi gas. Phys. Rev. Lett. 109, 095302 (2012)

    Article  ADS  Google Scholar 

  31. R.A. Williams, M.C. Beeler, L.J. LeBlanc, K. Jiménez-García, I.B. Spielman, Raman-induced interactions in a single-component fermi gas near an \(s\)-wave feshbach resonance. Phys. Rev. Lett. 111, 095301 (2013)

    Article  ADS  Google Scholar 

  32. Nathaniel Q. Burdick, Yijun Tang, Benjamin L. Lev, Long-lived spin-orbit-coupled degenerate dipolar fermi gas. Phys. Rev. X 6, 031022 (2016)

    Google Scholar 

  33. B. Song, C. He, S. Zhang, E. Hajiyev, W. Huang, X.J. Liu, G.B. Jo, Spin-orbit-coupled two-electron fermi gases of ytterbium atoms. Phys. Rev. A 94, 061604 (2016)

    Article  ADS  Google Scholar 

  34. L. Huang, Z. Meng, P. Wang, P. Peng, S.L. Zhang, L. Chen, D. Li, Q. Zhou, J. Zhang, Experimental realization of two-dimensional synthetic spincorbit coupling in ultracold fermi? gases. Nat. Phys. 12, 540–544 (2016)

    Article  Google Scholar 

  35. Zengming Meng, Lianghui Huang, Peng Peng, Donghao Li, Liangchao Chen, Xu Yong, Chuanwei Zhang, Pengjun Wang, Jing Zhang, Experimental observation of a topological band gap opening in ultracold fermi gases with two-dimensional spin-orbit coupling. Phys. Rev. Lett. 117, 235304 (2016)

  36. A.J. Olson, D.B. Blasing, C. Qu, C.H. Li, R.J. Niffenegger, C. Zhang, Y.P. Chen, Stueckelberg interferometry using periodically driven spin-orbit-coupled bose-einstein condensates. Phys. Rev. A 95, 043623 (2017)

    Article  ADS  Google Scholar 

  37. Yongping Zhang, Zhiqian Gui, Yuanyuan Chen, Nonlinear dynamics of a spin-orbit-coupled bose-einstein condensate. Phys. Rev. A 99, 023616 (2019)

  38. K. Jiménez-García, L.J. LeBlanc, R.A. Williams, M.C. Beeler, C. Qu, M. Gong, C. Zhang, I.B. Spielman, Tunable spin-orbit coupling via strong driving in ultracold-atom systems. Phys. Rev. Lett. 114, 125301 (2015)

    Article  ADS  Google Scholar 

  39. Yongping Zhang, Gang Chen, Chuanwei Zhang, Tunable spin-orbit coupling and quantum phase transition in a trapped bose-einstein condensate. Sci. Rep. 3, 1937 (2013)

    Article  ADS  Google Scholar 

  40. Y. Zhang, M.E. Mossman, T. Busch, P. Engels, C. Zhang, Properties of spincorbit-coupled boseceinstein condensates. Front. Phys. 11 (2016)

  41. L.D. Landau, E.M. Lifshitz, Quantum mechanics: non-relativistic theory (Pergamon Press, Oxford, 1977)

    MATH  Google Scholar 

  42. Y. Kayanuma, Role of phase coherence in the transition dynamics of a periodically driven two-level system. Phys. Rev. A 50, 843–845 (1994)

    Article  ADS  Google Scholar 

  43. C. Zhu, H. Nakamura, Two-state linear curve crossing problems revisited. iv. The best analytical formulas for scattering matrices. J. Chem. Phys. 101(6), 4855–4866 (1994)

    Article  ADS  Google Scholar 

  44. Yosuke Kayanuma, Stokes phase and geometrical phase in a driven two-level system. Phys. Rev. A 55, R2495–R2498 (1997)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

This work is supported by the National Natural Science Foundation of China (Contract No. 12005173, 12075193, and No. 11747018), by the Natural Science Foundation of Gansu Province (Grant No. 20JR10RA082), and by the China Postdoctoral Science Foundation (Grant No. 2020M680318).

Author information

Authors and Affiliations

Authors

Contributions

All the authors were involved in the preparation of the manuscript. All the authors have read and approved the final manuscript.

Corresponding author

Correspondence to Wen-Yuan Wang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, XX., Wang, WY. & Dou, FQ. Landau–Zener–Stückelberg–Majorana interference of a spin-orbit-coupled Bose–Einstein condensate. Eur. Phys. J. D 75, 150 (2021). https://doi.org/10.1140/epjd/s10053-021-00158-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjd/s10053-021-00158-9

Navigation